18. What is the “nine-points circle”?
19. Why is it so called?
20. Name the special nine points through which it passes.
21. What three regular figures can be used in filling up the space round a point? Ans. Equilateral triangles, squares, and hexagons.
22. If the sides of a triangle be 13, 14, 15, what are the values of the radii of its inscribed and escribed circles?
23. What is the radius of the circumscribed circle?
24. What is the radius of its nine-points circle?
25. What is the distance between the centres of its inscribed and circumscribed circles?
26. If r be the radius of a circle, what is the area of its inscribed equilateral triangle?—of its inscribed square?—its inscribed pentagon?—its inscribed hexagon?—its inscribed octagon?—its inscribed decagon?
27. With the same hypothesis, find the sides of the same regular figures.